GRE Questions

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18 tens 20 ones, the given stateent can be split into

18 tens = 18 x 10 = 180

20 ones = 20 x 1 = 20

Then add both => 180 + 20 = 200

Hence, 18 tens 20 ones = 200.

The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.

Relative speed = 72 -36 = 36 kmph = 36 x 5/18 = 10 mps.

Time required = d/s = 500/10 = 50 sec.

Acording to the above stated passage only the argument " The nearsightedness in the children is caused by the ...........visual stress required by reading and other class work." will be true

Here by observing the figure, 

we can complete the above incomplete cube with 2 cubes in 2 rows and 2 columns

=> 2 x 4 = 8.

Hence, with 8 small cubes we can complete the cube.

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120

For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120

So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120

Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

The given letter equation puzzle means that 

7 W of the W = 7 Wonders of the World.

For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9
Total number of zero in this range = 0

2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

1. Answer (c)

Each time we order 1, one apple is added to the basket but each time when 4 is ordered, one apple is removed from it.

Required number of apples = number of 1's - number of 4's = 6 - 4 = 2

2. Answer (d)

Each time we order 1, 2 or 3, one fruit is added to the basket but when ever we order 4, two fruits are removed from it.

Required number = Number of 1's + Number of 2's + Number of 3's - 2 x (Number of 4's)

= 6 + 6 + 7 - (2x4)
= 19 - 8
= 11.